FIG. 4 shows an example of a conventional signal separating and reproducing apparatus that processes acoustic signals. This structure has two channels for input signals. As shown in FIG. 4, the signal separating and reproducing apparatus 1000 includes two input terminals 1 and 2, a separation filter analyzing unit 3, a separation and reproduction filter calculating unit 4, a separation and reproduction filter unit 5, a separation and reproduction filter unit 6, four output terminals 7, 8, 9, and 10.
The signal separating and reproducing apparatus 1000 operates in the following manner. Individual channel input signals Xj(t) are supplied to the input terminal 1 and the input terminal 2. Here, j indicates the channel number (j=1, 2), and t indicates the time sample number. Both individual channel input signals are supplied to the separation filter analyzing unit 3.
The separation filter analyzing unit 3 separates acoustic and voice signals that are convoluted in the individual channel input signals. More specifically, the separation filter analyzing unit 3 performs a frequency transform on each of the individual channel input signals, so as to calculate a frequency sequence Xj(k,n). Here, k indicates the frequency component number (k=0, 1, . . . , N/2−1), N indicates the block length of the frequency transform, and n presents the frame number (n=0, 1, . . . ). The separation filter analyzing unit 3 regards every frequency component as an instantaneous mixture, and carries out an independent component analysis (hereinafter referred to as the “frequency region independent component analysis”), so as to calculate a separation filter frequency characteristics matrix W(k).
The separation filter frequency characteristics matrix W(k) is a matrix formed with two rows and two columns, with Wij(k) being the elements of the matrix as shown in the following equation. Here, i presents the separation signal number (i=1, 2), and j indicates the channel number.
                    {                  Math          .                                          ⁢          1                }                                                                      W          ⁡                      (            k            )                          =                  (                                                                                          W                    11                                    ⁡                                      (                    k                    )                                                                                                                    W                    12                                    ⁡                                      (                    k                    )                                                                                                                                            W                    21                                    ⁡                                      (                    k                    )                                                                                                                    W                    22                                    ⁡                                      (                    k                    )                                                                                )                                    (        1        )            
The frequency region independent component analysis is a technique for separating linearly-coupled signals, based on the statistical independence between signals. Such a technique is disclosed in the later described Non Patent Literature 1, for example. It is known that such a frequency region independent component analysis has the problem that the order of separation signal numbers (i=1, 2) of the matrix elements Wij(k) at the respective frequency components becomes uncertain, and the problem that the sizes of the matrix elements Wij(k) at the respective frequency components become uncertain. To eliminate the uncertainty about the order, which is the former problem, there is a technique by which the continuity of the frequency direction is used, or a technique by which the arrival direction is used, for example.
To solve the problem about the sizes of the matrix elements, which is the latter problem, the following technique has been known. In a case where a separation and reproduction filter frequency characteristics matrix Mi(k) is generated by combining the separation filter frequency characteristics matrix W(k) and the reproduction filter frequency characteristics matrix W−1(k), which is the inverse matrix formed from the separation filter frequency characteristics matrix W(k) at the respective frequencies, uncertainty is not caused in the sizes of the matrix elements. The separation and reproduction filter frequency characteristics matrix Mi(k) is expressed by the following equation (2):Mi(k)=W−1(k)·Pi(k)·W(k)i=1,2  (2)
Here, only the element on the ith row and the ith column of the matrix Pi(k) is “1”, and the other elements of the matrix Pi(k) are “0”, as expressed by the following equation (3):
                    {                  Math          .                                          ⁢          2                }                                                                                                P              1                        ⁡                          (              k              )                                =                      (                                                            1                                                  0                                                                              0                                                  0                                                      )                          ,                                  ⁢                                            P              2                        ⁡                          (              k              )                                =                      (                                                            0                                                  0                                                                              0                                                  1                                                      )                                              (        3        )            
A matrix W′(k) that is formed by adding coefficients a(k) and b(k) indicating the size uncertainties of the matrix elements of the separation filter frequency characteristics matrix W(k) to the separation filter frequency characteristics matrix W(k) is expressed by the following equation (4):
                    {                  Math          .                                          ⁢          3                }                                                                                  W            ′                    ⁡                      (            k            )                          =                              (                                                                                a                    ⁡                                          (                      k                      )                                                                                        0                                                                              0                                                                      b                    ⁡                                          (                      k                      )                                                                                            )                    ·                      W            ⁡                          (              k              )                                                          (        4        )            
The separation and reproduction filter frequency characteristics matrix M′i(k) using the above matrix W′(k) can be expressed by the following equation (5):
                    {                  Math          .                                          ⁢          4                }                                                                                                                                  M                  i                  ′                                ⁡                                  (                  k                  )                                            =                            ⁢                                                                                          W                      ′                                                              -                      1                                                        ⁡                                      (                    k                    )                                                  ·                                                      P                    i                                    ⁡                                      (                    k                    )                                                  ·                                                      W                    ′                                    ⁡                                      (                    k                    )                                                                                                                          =                            ⁢                                                                    W                                          -                      1                                                        ⁡                                      (                    k                    )                                                  ·                                                      (                                                                                                                        a                            ⁡                                                          (                              k                              )                                                                                                                                0                                                                                                                      0                                                                                                      b                            ⁡                                                          (                              k                              )                                                                                                                                            )                                                        -                    1                                                  ·                                                      P                    i                                    ⁡                                      (                    k                    )                                                  ·                                  (                                                                                                              a                          ⁡                                                      (                            k                            )                                                                                                                      0                                                                                                            0                                                                                              b                          ⁡                                                      (                            k                            )                                                                                                                                )                                ·                                  W                  ⁡                                      (                    k                    )                                                                                                                                          =                                ⁢                                                      W                                          -                      1                                                        ⁡                                      (                    k                    )                                                              ⁣                              ·                                                      P                    i                                    ⁡                                      (                    k                    )                                                  ·                                  W                  ⁡                                      (                    k                    )                                                                                                                          =                            ⁢                                                M                  i                                ⁡                                  (                  k                  )                                                                                        (        5        )            
As is apparent from the above, the separation and reproduction filter frequency characteristics matrix does not contain uncertainty about the sizes of the matrix elements.
The separation and reproduction filter calculating unit 4 performs an operation to eliminate the uncertainty about the sizes by the above described technique. More specifically, the reproduction filter frequency characteristics matrix W−1(k) is calculated by transforming the separation filter frequency characteristics matrix W(k) into an inverse matrix at the respective frequencies. The matrix W−1(k) and the original matrix W(k) are then combined, so that the above mentioned separation and reproduction filter frequency characteristics matrix Mi(k) is calculated. Further, an inverse frequency transform is performed on the separation and reproduction filter frequency characteristics matrix Mi(k) for each of the matrix elements Mij(i)(k) (i=1, 2; I=1, 2; j=1, 2), so as to calculate eight separation and reproduction filter coefficients Mij(i)(s) (s=0, 1, . . . , N−1). Here, I indicates the channel number of each separation signal (I=1, 2).
The separation and reproduction filter unit 5 implements filtering on input signals xj(t) (j=1, 2) for the respective channels, with use of four separation and reproduction filter coefficients Mij(1)(k) (I=1, 2; j=1, 2). Synthesized signals zI(1)(t) of the respective channels are then calculated according to the following equation (6). Here, “*” indicates a convolution operation.zi(1)(t)=mI1(1)(s)*xi(t)+mI2(1)(s)*x2(t)I=1,2  (6)
Like the separation and reproduction filter unit 5, the other separation and reproduction filter unit 6 implements filtering on input signals xj(t) (j=1, 2) for the respective channels, with use of four separation and reproduction filter coefficients Mij(2)(k) (I=1, 2, j=1, 2). Synthesized signals zI(2)(t) of the respective channels are then calculated according to the following equation (7).zI(2)(t)=mI1(2)(s)*xI(t)+mI2(2)(s)*x2(t)I=1,2  (7)
As a result of the above operation, the output terminal 7 outputs the synthesized signals zI(1)(t) of the corresponding channel, the output terminal 8 outputs the synthesized signal z2(1)(t) of the corresponding channel, the output terminal 9 outputs the synthesized signals zI(2)(t) of the corresponding channel, and the output terminal 10 outputs the synthesized signals z2(2)(t) of the corresponding channel.
{Citation List}
{Non Patent Literature}
{NPL 1} Shuxue. Ding, Masashi Otsuka, Masaki Ashizawa, Teruo Niitsuma, Kazuyoshi Sugai, “Blind source separation of real-world acoustic signals based on ICA in time-frequency-domain”, Technical Report of IEICE, SP2001-1, p.p. 1-8, April 2001